title: Novel algorithm of large-scale simultaneous linear equations.
abstract: We review our recently developed methods of solving large-scale simultaneous linear equations and applications to electronic structure calculations both in one-electron theory and many-electron theory. This is the shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace, and the most important issue for applications is the shift equation and the seed switching method, which greatly reduce the computational cost. The applications to nano-scale Si crystals and the double orbital extended Hubbard model are presented.
authors.affiliation: Center for Research and Development of Higher Education, The University of Tokyo, Bunkyo-ku, Tokyo, 113-8656, Japan.
authors.forename: T
authors.initials: T
authors.lastname: Fujiwara
authors.forename: T
authors.initials: T
authors.lastname: Hoshi
authors.forename: S
authors.initials: S
authors.lastname: Yamamoto
authors.forename: T
authors.initials: T
authors.lastname: Sogabe
authors.forename: S-L
authors.initials: SL
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D053768:Metal Nanoparticles / Q000737:chemistry*; D008954:Models, Biological; D012825:Silicon / Q000737:chemistry*; D012984:Software
chemical_list: D012825:Silicon